Efficient estimation by FEA of machine tool distortion due to environmental temperature perturbations

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ContentslistsavailableatSciVerseScienceDirect

Precision

Engineering

jou rn a l h o m e pa g e :w w w . e l s e v i e r . c o m / l o c a t e / p r e c i s i o n

Efﬁcient

estimation

by

FEA

of

machine

tool

distortion

due

to

environmental

temperature

perturbations

Naeem

S. Mian

∗

,

S. Fletcher,

A.P.

Longstaff,

A. Myers

CentreforPrecisionTechnologies,UniversityofHuddersﬁeld,Queensgate,HuddersﬁeldHD13DH,UK

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received14June2012

Receivedinrevisedform5October2012 Accepted12October2012

Available online 24 October 2012 Keywords:

Finiteelementanalysis Precision

Machinetoolaccuracy

Environmentaltemperatureﬂuctuations Ambienttemperature

Thermalerror

a

b

s

t

r

a

c

t

Machinetoolsaresusceptibletoexogenousinﬂuences,whichmainlyderivefromvaryingenvironmental

conditionssuchasthedayandnightorseasonaltransitionsduringwhichlargetemperatureswingscan

occur.Thermalgradientscauseheattoﬂowthroughthemachinestructureandresultsinnon-linear

structuraldeformationwhetherthemachineisinoperationorinastaticmode.These

environmen-tallystimulateddeformationscombinewiththeeffectsofanyinternallygeneratedheatandcanresult

insigniﬁcanterrorincreaseifamachinetoolisoperatedforlongtermregimes.Inmostengineering

industries,environmentaltestingisoftenavoidedduetotheassociatedextensivemachinedowntime

requiredtomapempiricallythethermalrelationshipandtheassociatedcosttoproduction.Thispaper

presentsanovelofﬂinethermalerrormodellingmethodologyusingﬁniteelementanalysis(FEA)which

signiﬁcantlyreducesthemachinedowntimerequiredtoestablishthethermalresponse.Italsodescribes

thestrategiesrequiredtocalibratethemodelusingefﬁcienton-machinemeasurementstrategies.The

techniqueistocreateanFEAmodelofthemachinefollowedbytheapplicationoftheproposed

method-ologyinwhichinitialthermalstatesoftherealmachineandthesimulatedmachinemodelarematched.

Anaddedbeneﬁtisthatthemethoddeterminestheminimumexperimentaltestingtimerequiredona

machine;productionmanagementisthenfullyinformedofthecost-to-productionofestablishingthis

importantaccuracyparameter.Themostsigniﬁcantcontributionofthisworkispresentedinatypical

casestudy;thermalmodelcalibrationisreducedfromafortnighttoafewhours.Thevalidationworkhas

beencarriedoutoveraperiodofoverayeartoestablishrobustnesstooverallseasonalchangesandthe

distinctlydifferentdailychangesatvaryingtimesofyear.Samplesofthisdataarepresentedthatshow

thattheFEA-basedmethodcorrelatedwellwiththeexperimentalresultsresultingintheresidualerrors

oflessthan12␮m.

1. Introduction

Theshopﬂoorenvironmentwhere aCNCmachineislocated

canbeofparamountimportanceforaccuracyofmanufacturing.

Temperaturecontrolledenvironmentsrequirehighcapital

invest-mentsand runningcosts,which areundesirableand sometimes

impractical.Inenvironmentswherethetemperatureisnot

con-trolled,thechangingdayandnightcyclictransitionsandmyriad

othersources[1,2]cancauseambienttemperaturestovary

sig-niﬁcantlybothinmagnitudeandrate-of-change.Thesetemporal

ﬂuctuationscancausespatialthermalgradientsinamachinetool;

theheatﬂowthroughthestructureovertimecausesnon-linear

thermaldeformations.Severalresearchprojectshave been

con-ductedtoidentify,predictandcompensatetheoveralleffectofthe

thermaldistributioninamachinetoolbutwithmainemphasison

∗ Correspondingauthor.

E-mailaddress:[email protected](N.S.Mian).

solvingtheeffectofinternallygeneratedheat,particularlyfromthe

mainspindleandduringthemachiningprocesses.Forexample,

Hao[3]usedageneticalgorithm-basedbackpropagationneural

network(GA-BPN)methodusing16thermistorsplacedatthe

spin-dle,headstock,axisleadscrewandonthebedofaturningmachine

tocompensatedynamicandhighlynonlinearthermalerror.Only

oneambienttemperaturesensorwasusedwhichmaynotbe

suf-ﬁcient tocapturedetailedenvironmentalbehaviouraround the

machinevicinity.Theauthorreportedthethermalerror

compen-sationimprovementof63%.Furtherreductioncouldbepossibleif

detailedexternalenvironmentaltemperatureswingswere

consid-ered.Similarly,researchfromYangetal.[4]testedanINDEX-G200

turningcentreandusedMRAtechniquetopredictitsthermal

accu-racy.Theanalysisresultshowedthatthethermalerrorrangefor

radiusdirectiononthatmachinewasapproximately18␮m,higher

thanexpected.14thermalsensorswereinstalledingroupsand

onlyoneambientsensorwasused.Whilemodelling,six

temper-aturegroupswithvariableswereconstructedandthemodelwas

assumedtobealinearfunctionfortheenvironmentaltemperature

http://dx.doi.org/10.1016/j.precisioneng.2012.10.006

Open access under CC BY license.

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accuracyimprovementsof±10␮mto±3␮m.However,themodel

trainingtimesandmachinedowntimeareaccountableissueswith

thisresearch.Oneoftheregressiontechniquesknownas

ortho-gonalregression techniquewasemployedby Duet al.[6].This

techniquewasappliedtomorethan100turningcentresofthesame

typeandspeciﬁcations.Itwasfoundthatthetechniquewasableto

reducethecuttingdiameterthermalerrorfrom35␮mto12␮m.

Thetechniquewasstatedasrobustduetoitsyearround

repeat-ableimprovementinaccuracy.Theaccuracyisexpectedtoincrease

iflongtermshopﬂoorenvironmentaltemperaturesﬂuctuations

wereconsidered.

Many researchers drew attention towards the

environmen-talthermaldriftsinmachinetoolswhicharisefromavarietyof

sourceswhiletheyemphasisedthemachinedowntimerequired

fordetailedenvironmentaltestingaswellasanalysingthe

mod-ellingmethodsandmodellingtime.RakuffandBeaudet[7]drew

attentiontotheimportanceandeffectoftheenvironmental

tem-peraturevariationerror(ETVE)whileconductingacuttingtestof

24honadiamondturningmachine.Theresearchsuggestedthe

provisionoftemperaturecontrolledenclosuresforthemachineto

avoidexternalthermaldriftstoimprovetheaccuracyoftheprocess

control.Fletcheretal.[8]providedusefulinformationaboutcyclic

environmentalﬂuctuationsanddriftswith50%reductioninerror

overa65htest,butdrewattentiontothedetrimentalamountof

machinedowntimeforthethermalcharacterisationtests.Longstaff

etal.[2]showedseveraltestsconductedforthethermalerror

mea-surementsproducedbytheenvironmentalﬂuctuationscombined

withlongtermmachining.Theauthorsalsohighlightedsome

unex-pected,rapidﬂuctuationsoftheenvironmentwithitseffectonthe

accuracyofthemachine.Theyalsohighlightedthemachine

down-timeissuesrelatedwiththemeasurements.Jedrzejewskietal.[9]

discussesthecomplexitiesinvolvedwithimprovingthedesignof

amachinetoolwhenconsiderationsofreducingthermalerrorare

infocus.Ahighlyaccuratethermalmodelofthemachineis

pre-sentedand consideration ofvarious parameters contributingto

thethermalbehaviour.Forexample,thedesigncriteriaconsidered

theeffectsofenvironmentalvariationsfor2.5days,thermaleffects

aroseduetothepresenceofguardingandbearingsetsofhighspeed

spindles.Quartzstraightedgesweremodelledforenvironmental

effectaftermountingonthemachinecentresupportbeam.Itwas

foundthatthestraightedgeﬁxedontheleftsideproducedthe

lowesterroroftheotherthreelocationstested.Theinformation

relatedtotheFEAsuchasthemodellingtimewasnotclearandthe

operatingconditionswerenotclearlystated.Aconcernshownby

BringmannandKnapp[10]abouttheeffectofthermaldriftwhile

showinghowincreasingthenumberofmeasurementpoints(from

4to60)canleadtoreduceduncertaintiesandhigheraccuracyfor

identiﬁedlocationerrorsoftherotaryC-axis.Theauthorreported

thatthefurtherincreaseinthemeasurementpointsonlyleadsto

limitedimprovementsasitcanleadtoextratimeformeasurement

whichincreasestheuncertaintyofthethermaleffectarisingfrom

environmentalorambienttemperaturechangesuntilthe

measure-mentiscomplete.

Itisapparentfromthediscussionthatagreatemphasishasbeen

giventocontrolthethermaleffectsmainlyarisingduetointernal

tool.Theproblemisexacerbatedsincethescopeofconditions

dur-ingwhichtestdatacanbeacquiredisverylimitedcomparedto

truevariationoverfacilityoperationsandnaturalseasons.

Thispaperpresentsanovelofﬂineenvironmentalthermalerror

modelling method based on FEAthat signiﬁcantly reducesthe

machinedowntimerequiredforeffectivethermalcharacterisation.

Theproposedmodellingmethodwastestedandsuccessfully

vali-datedonaproductionmachinetooloverayearperiodandfound

tobeveryrobust(inthispaper,samplesofdatameasuredduring

twoseasonsarepresented).Thevalidationconﬁrmedthepotential

ofthismethodtoreducethemachinedowntimenormallyrequired

fortheenvironmentaltestingfromafortnighttoafewhours.The

paperalsohighlightstheeffectsofseasonalenvironmental

tem-peraturechangesinamachinetoolandthepresenceofvertical

temperaturegradientswithinashopﬂoorenvironment.Thepaper

alsodescribeson-machinemeasurementmethodstoacquirethe

required data efﬁciently using strategically placed temperature

sensorsduringanyconvenientmaintenancescheduleperiod.

2. Proposedmethod

Ingeneral,environmentaltemperaturechangesarenotasrapid

asthosefrominternallygeneratedsourcessuchasspindles.

Addi-tionally,therecanbeseveraldifferentstructuralresponseswhich

requiredifferent metrology equipmentto measure that cannot

beusedconcurrently.Therefore,environmentaltestingnormally

takesfromtwodaystoseveralweekstoacquiresufﬁcientdata

toestablishthevariousrelationshipsbetweenvarying

tempera-tureproﬁlesandtheresponseofthemachine.Toovercomethe

machinedowntimeissue,anovelmodellingmethodologybased

onatwo-stageFEAisproposedinthispaperwhereaComputer

AidedDrawing(CAD)modelofthemachineiscreatedintheFEA

software(inthisstudyAbaqus6.7-1/Standardwasused)[11].This

isfollowedbyadeterminationoftheinitialthermalstateforthe

FEAmodel,akeymethoddevelopedinthisresearch,whichwill

establishaclosematchoftherealinitialthermalconditionofthe

machinebeforeconductingenvironmentalsimulations.

2.1. FEAmodelling

Amachine toolis, inpractice,rarelyatthermal equilibrium.

Consequently,establishingtheinitialconditionsfortheFEA

sim-ulationofenvironmentalchangepresentsa signiﬁcantproblem

asitadverselyaffectsthecomparisonoftheFEAand

experimen-talresults.To representtherealistic initialthermalstateofthe

machine structure isa challenging taskif therealtemperature

gradientsaretobemeasuredandappliedtothemodel.

Experi-mentally,theapplicationoftheindividualtemperaturesensorsat

locationswithinthemachinestructuralloopislaboriousandprone

touncertainty inlocatingsensitiveareas.In contrasttothermal

errorfromrunningthemachinewheretheheatsourcesareeasy

toidentifyforapplicationofthesensors,environmentalchanges

affectthewholestructure.However,evenifthisisachieved,

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Fig.1.GeneratedCADmodelofthemachineassemblywithZaxisheadmovedupcomparedto[1]inessencetopresentanewermodelcorrespondingtonewtestconditions.

remainschallenging.Sectioningthemodelledpartsinthesoftware

andapplyingindividualtemperaturestothemmayrepresentthe

initialthermalstatebutitisastrenuoustaskandmaycause

incor-recttemperaturegradientsduetosectionjoints.Thisproblemis

solvedbytheproposednovelmethodwhichdeterminestheinitial

thermalstatefor themachine modelandalsoprovidesan

esti-mateoftheminimumtimerequiredforanenvironmentalteston

amachine(Section2.3).

2.1.1. Machinemodel

Amodelofthemachineisrequired.Forthecasestudymachine,

amodel describedbytheauthors[1]withrespecttointernally

generatedheatwasusedtoestimatethelong-termenvironmental

response.Themachinewasaprecision3-axisVerticalMachining

Centre(VMC)withaccuracyupto3␮m;testedby

manufactur-ingaNAS-979component[12].Simpliﬁedmodelsofthemachine

wereusedtocarryoutofﬂinesimulationsoftheenvironmental

behaviourofthemachine,detailsofwhichareshowninFig.1.

The model was meshed using tetrahedral, hexahedron and

hexahedron dominated (hexahedron/wedge) elements where

applicableusingAbaqusdefaultmeshingtechniquewhichrevealed

thetotalof49,919elementsand20,418nodes.Fig.2showsthe

meshedassemblyofthemachine.Allsimulationsareperformed

astransientthermalsimulations wherechangingdata fromthe

temperaturessensorsisappliedinthesoftwareusingthetabular

amplitudetechnique.

2.2. Estimationofinitialthermalstateofthemachine

Generally,priortothestartofanytest,themachineelements

exhibitvariationsintemperatureduetotheexistenceoftemporal

andspatialthermalgradients.Inparticular,verticaltemperature

gradientshavebeenfoundtobesigniﬁcant[2,13].Asaresult,it

isunfeasibletoaccuratelysetinitialtemperaturesofthe

compo-nentsintheFEAsoftwaretomatchreality.Anewtechniqueofa

two-stagesimulationinAbaqushasbeendevisedandappliedto

solvethis problem.Theﬁrststagesimulationineffectwill

esti-matethetimespanrequiredbyamachineFEAmodelto‘absorb’

theglobally appliedtemperaturefora temperaturechange

rep-resentingthemaximumvariationlikelytooccuronthemachine

structure.Thistimespanistermedasthe‘settlingtime’and

repre-sentsthetemperaturerisetimeforthesteadystatemachinemodel

when‘absorbing’theappliedtemperatures.Thesettlingtimeisalso

representativeoftheminimumtimerequiredforon-machine

test-ingwhichisexplainedinSection2.3.Thisisfollowedbythesecond

stageofnormalenvironmentalsimulationthatcanbeusedforerror

modellingandcomparedwithexperimentforvalidation.

Tosetupthesimulation, a standardshopﬂoortemperature

of 20◦C was appliedas a uniformparametertothe fullmodel

of the machine as a ‘Predeﬁned Field’in theAbaqus software.

Since thispaperfocuses onanattempttoprovethe

methodol-ogyandmaintainrelativesimplicityintheFEAprocess,theentire

modelwasappliedwiththeconvectiveheattransfercoefﬁcientof

6Wm−2◦C−1[1]whichisanaveragedvalueofthevariousheat

transfercoefﬁcientscalculatedexperimentally[1].Itis

acknowl-edgedthatmoredetailedapplicationofsurfacespeciﬁccoefﬁcients

couldimprovesimulationaccuracy(seeSection4.2).Toestimate

thetime,themodelwassimulateduntilitachieveda

tempera-turechangeindicativeofthevariationbetweentheglobalassumed

20◦Candtheappliedtemperature.Asimulationwascarriedout

with1◦C temperature changetoestimatethetemperaturerise

time.

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Fig.3. Settlingtimeof12.5hwasrevealedforthismachine’sFEAmodel.

Attheendofthesimulationthetemperaturethroughoutthe

machinemodelwasuniform;thisensuredtheselectionofarandom

nodetoplotthesettlingtime.Thesimulatedresultrevealedthat

themachinemodelachieved99.99%ofthe1◦Ctemperaturechange

fromitsinitialtemperatureof20◦Cin12.5hasshowninFig.3.

Thissettlingtimesuggeststhatbecausethemachineinitial

ther-malstateisunknownatthestartofthesimulation,thismachine

FEAmodelrequiresthissettlingtimetoabsorbtheappliedrecorded

environmentaltemperaturedataattheendofwhichthe

temper-aturedistributionshouldbesynchronisedwiththerealmachine

thermalstate.

2.3. Modelcalibration

Themodelcalibrationsequenceswiththedeterminationofthe

settlingtimeattheﬁrstplace.Thesettlingtimesuggeststhe

min-imumenvironmentaltestingtimerequiredforthismachinetool

whichisanimportantparameterforboth;theproduction

man-agementtoestimatethecost-to-productionandfortheaccuracy

ofFEAresultsespeciallywhenachievingtheinitialthermalstate

ofthemachineFEAmodelbeforeconductingenvironmental

sim-ulations.Thereforetheenvironmentaltesttobeconductedonthe

machinemustensurethatthesettlingtimeiscovered.Thetestthen

mustbecontinuedoveralongperiodsuchastwoorthreedaysto

establishtherelationshipbetweenthemachinethermalbehaviour

andenvironmentalﬂuctuations occurringwithintheshopﬂoor

duringthesecondstagesimulation.Theambientsensorsusedto

recorddatamustbeleftsituatedinordertorecordcontinuously

whilethemachineisinoroffproduction.Sincethedetermination

ofthesettlingtimeisanofﬂineprocessthereforepracticallyno

ationerror(ETVE)[14]testswereconductedonthe3-axisVMCover

aperiodofafullyearnotonlytovalidatebuttoconﬁrmthe

robust-nessoftheproposedmethodology;howeversamplesofdatafrom

twoseasons(summerandwinter)arepresented.Three-day

(con-secutive)testingperiodwasselectedtoensurethesetting time

(12.5h)datarecordingaswellastohighlightthermalbehaviour

duringnormal24hperiodsonanominallystaticmachinetool.This

meansthatthemachinedriveswereinactivetoavoidfeedback

cor-rectionfromthepositionencoders;inessencetoobtainthetrue

deformationofmachinestructure.Themodelofthemachinewas

notmodiﬁedinanywayduringthisvalidationphase.

3.1. Temperatureanddisplacementsensorlocations

Themachinewasalreadyequippedwith65temperature

sur-facesensorsinuniquestrips[15]formeasuringdetailedthermal

gradientscausedbytheinternalheatsources.Additionallyseven

surfacesensorswereplacedonthecolumntotrackthe

environ-mentaltemperaturegradientsdistributioninthistallstructureand

onesurfacesensoronthebase.Threeambientsensorswereplaced

insidethemachine,atthemachinecolumnandadjacenttothe

basetomeasureenvironmentaltemperaturevariations.Five

non-contactdisplacementtransducers(NCDTs)wereplacedarounda

testmandreltomonitorthedisplacementsandtiltofthetest

man-drelin the X, Yand Zaxisdirections. A 400mm postmade of

invarwasusedtosupporttheNCDTs.Invarisasteelalloywitha

verylowcoefﬁcientofthermalexpansion(1.2␮mm−1K−1)which

reducestheeffectsofchangingenvironmentaltemperature.

Sen-sorplacementsareshown inFig.4.WithreferencetotheBase

sensor,theinsideambientsensorwasdisplacedbyapproximately

1mverticallyand0.5mhorizontallywhilethecolumnsensorwas

approximately1.2mverticallyand2mhorizontallyapart.

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Fig.5. Temperatureproﬁlesobtainedover3daysperiod(summertest).

3.2. Summertest

Thetemperatureinformationobtainedfromthesurfacesensor

ontheSpindleBossandtheambientsensorsfora 3dayperiod

areshownintheFig.5.Atthestartofthetest,theexistenceof

averticaltemperaturegradientaroundthemachineof1◦Cwas

measuredbetweenthebaseambientsensorandthecolumn

ambi-entsensorwhichcreatestheaforementionedcomplexinitialstate.

Itmayalsobeofinterestthattheverticaltemperaturedifference

betweenthecolumnambientsensorandthebaseambientsensor

ﬂuctuatedtoapproximately2.5◦Crangeoverthetestspanwhich

isfurtherevidenceoftemperatureinstabilitywithintheshopﬂoor

environmentaltemperaturearisingfromvarioussourcessuchas

thedayandnighttransitions.Temperatureﬂuctuationsalsooccur

whenopeningandclosingworkshopdoors.

Fig.6showsthemeasuredinsideairtemperatureandthe

dis-placement of the mandrel in the Y-axis and Z-axis. The Y-axis

displacement followed the temperature variation quite closely

whereastheZ-axisdisplacementlaggedthetemperaturebyupto

3.6hatsomeplaces.TheanalysisontheYaxisresults(usingthe

topandbottomNCDTs)revealeda30␮m/mtiltpresentwhichis

likelytohavebeencausedbynon-uniformdistortionsinthe

com-plexgeometryofthestructureresultingintherapidresponseto

thetemperaturevariation;comparedwiththeslowresponseof

theZ-axiswhichispossiblycontributedfrompureexpansion.The

overalldisplacementrangewasapproximately12␮mforthe

Y-axisandapprox.28␮mfortheZ-axiswiththeoveralltemperature

swingofapproximately4◦Cover3days.TheX-axisresultswere

negligible,duetothesymmetryofthemachineinthisdirection,

andthereforenotpresented.

Thistestvalidatesthehypothesisthatenvironmental

ﬂuctua-tioncausesthermal distortionsinmachinestructureandproves

thedeteriorationintheaccuracyofamachinetool.Itwasalso

iden-tiﬁedthatverticaltemperaturegradientsinashopﬂoorvarywith

heightwhichcanbecriticaltolargeand/ortallmachines.

Fig.6.YandZaxesdisplacementsandtheenvironmentaltemperaturemeasured insidethemachine(summertest).

Fig.7. Temperaturegradientsacrossthestructureaftertheﬁrststage(12.5h)that representtheactualinitialthermalstate(summertest)– (NT11– nodal tempera-tures–◦_C).

3.3. Validatingsettlingtimemethodology

Thesettlingtimeforthismachinemodelwasdeterminedtobe

12.5hthereforedatacoveringthistimespanwasselectedfromthe

measuredambientdataandusedintheﬁrststagesimulation.As

mentionedpreviously,thetemperaturedatawasappliedasa

tran-sientfunctioninthesoftwareusingtabularamplitudetechnique

forbothsimulationstages.Temperaturedatafromthebasesensor

wasappliedtothebase,informationfromtheinside

environmen-talsensor wasapplied tothecarrier/spindle/tool and thetable

andtemperatureinformationobtainedfromthecolumnambient

sensorwasappliedtothecolumn.Theresultfromtheﬁrststage

simulationmustprovidenotonlythecorrecttemperatureproﬁle

butalsothecorrectthermal memorytomatchthestarting

con-ditionoftherealmachine.Itmustbenotedthatthesimulations

werecarriedoutusingonlytheambientdatawhichcanbecaptured

withoutmachinedowntime,thesurfacesensorsareonlyusedto

compareandcorrelatethesimulatedresults.Fig.7showsthe

sim-ulatedtemperaturegradientsacrossthestructureafterthesettling

timewhichshouldrepresenttherealsurfacetemperature

gradi-entsafterthe12.5hspanwaslapsed.Thepredictedinitialthermal

statewasrevealedtobewithin±0.2◦_C_range_measured_at_points

wheresurfacesensorswereplacedandshowninTable1

Afterthesettlingtimesimulation,anormalenvironmental

sim-ulationis then runin thesecond stageusing theremainderof

therecordedenvironmentaltemperaturedata.Themeasuredand

simulatedproﬁleresultswereplottedforthemainsecondstage

simulation.Thesimulatederrorisobtainedasthedifferencein

dis-placementbetweenthetableandthetool(testmandrel).Compared

Table1

Comparisonofmeasuredandsimulatedsurfacetemperaturesafter12.5h(summer test). Structure Measured temperature (◦C) Simulated temperature (◦C)

Spindlebosssurface 24.1 24

Columnsurface 24 23.9

Carrierheadsurface 24.2 24.0

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Fig.8. CorrelationbetweenthemeasuredandsimulatedYaxisdisplacementwith settlingtimeremoved.

Fig.9. CorrelationbetweenthemeasuredandsimulatedZaxisdisplacementwith settlingtimeremoved.

tothemeasuredresults,thecorrelationswere60%fortheY dis-placementproﬁles(Fig.8)and63%fortheZdisplacementproﬁles

(Fig.9).Theresidualerrorswerelessthan5␮mfortheYaxisand

lessthan11␮mfortheZaxis.Includingthesettlingtime,separate

simulationsfortemperatureanddisplacementtookapproximately

30and40minrespectively(70minintotal).Thecomputerusedhad

typicalPCspeciﬁcations:AMDPhenom9950Quadcore2.60GHz

processor,4GBRAM,NVIDIAGeForce9400GTgraphicscardand

WindowsXP32bitoperatingsystem

4. Wintertest

Tofurthervalidatetherobustnessofthismodelling

methodol-ogy,anotherthree-daytestwascarriedouttoobservethemachine

behaviourinthewinterseason.Theworkshopexperienced

typ-icalsingleshiftworkshopheatingpatternsoftenencounteredto

maintaincomfortableenvironmentaltemperatureforthemachine

operators.Themachineandmeasurementtestconditionswerethe

sameasforthesummerenvironmenttest.

Thetemperatureinformationobtainedfromtheambient

sen-sors and thespindle boss surface sensor are shown in Fig. 10.

Thistime the verticaltemperature differencebetween the

col-umnambientsensorand thebaseambientsensorﬂuctuatedto

Fig.10. Temperaturedataobtainedover3daysperiod(wintertest).

Fig.11.YandZaxesdisplacementsandtheenvironmentaltemperaturemeasured insidethemachine.

approximately3◦Crangeoverthetestspanwhichelaboratesthat

evenverticaltemperaturedifferencechangeswithinsimilar

verti-caldistancesindifferentseasons.Thespikesaresuspectedtobe

fromtheshortperiodsforopeningofworkshopdoorsfor

deliv-erieswhichcausedtheshopﬂoorenvironmentaltemperatureto

decrease.

Fig.11showsthemeasuredinsideairtemperatureand

defor-mationof themachine in theYaxis andZaxis directions.The

movementofbothaxesfollowedthetemperaturevariationwhile

theZaxisdisplacementfollowedbutwithapproximately5hlag

thistime.Theoverallmovementis18␮mintheYaxisand35␮m

intheZaxisforanoveralltemperatureswingofapproximately

5◦C overthe3days.Thisincreasewasexpectedbecauseofthe

exaggerateddayandnightsheatingtransitions.

Fig.12.Temperaturegradientsacrossthestructureaftertheﬁrststage(12.5h)that representtheactualinitialthermalstate(wintertest).

Table2

Comparisonofmeasuredandsimulatedsurfacetemperaturesafter12.5h(winter test).

Structure Measured

temperature(◦C)

Simulated temperature(◦C) Spindlebosssurface 21.7 21.7

Columnsurface 21 20.9

Carrierheadsurface 21.6 21.6

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Table3

Summaryoftheresults.

Ydrift(␮m) Ymodelerror(␮m) Yimprovement(%) Zdrift(␮m) Zmodelerror(␮m) Zimprovement(%)

Summer 12 4.6 60 28 10 63

Winter 18 6.3 63 35 11.7 67

Fig.13.CorrelationbetweenthemeasuredandsimulatedYaxisdisplacementwith settlingtimeremoved.

4.1. FEAsimulations(ofﬂineassessments–wintertest)

Asimilarprocedurewasfollowedforsimulatingthemodel.For theﬁrststage,12.5hoftherecordeddatawasusedforthesettling timeasbefore,followedbytheenvironmentalsimulationinthe secondstage.Fig.12showsthesimulatedtemperaturegradients

acrossthestructureafterthesettlingtimewhichrepresentsthe

realsurfacetemperaturegradientsafterthe12.5hspanwaslapsed.

Thepredictedinitialthermalstatewasrevealedtobewithin±0.2◦_C

rangemeasuredatpointswheresurfacesensorswereplacedand

showninTable2.

4.1.1. Wintertestcorrelations

Thesimulatedresultscorrelatewellwiththemeasuredproﬁle

being63%fortheYmovementproﬁles(Fig.13)and67%forthe

Zmovementproﬁles(Fig.14).Theresidualerrorswerelessthan

7␮minYandlessthan12␮minZ.

Thewintertestnotonlyvalidatedthecapabilityofthemodelling

methodologybutalsoconﬁrmeditsrobustness.Developmentof

theCADmodel,obtainingthesettlingtimeandFEA

environmen-talsimulationsareconductedofﬂine.Thetemperaturesensorscan

beinstalledin anyconvenientmaintenance scheduleand

envi-ronmentaltemperaturedatacanberecordedwhilethemachine

in production therefore is non-invasive to production and cost

effectiveasgenerallynomachinedowntimeisinvolved.Itisalso

highlightedthat12.5hofsettlingtimecanberepresentativeofa

minimumtimerequiredfortemperaturedataacquisitionwhich

canberecordedwhilethemachineisinproduction.

Fig.14.CorrelationbetweenthemeasuredandsimulatedZaxisdisplacementwith settlingtimeremoved.

4.2. Summaryofresults

AnFEA-derivedthermalmodelofthemachinewascreatedin

thesummerusinga12.5hsettlingtimemethodology.This

method-ologyhasbeenvalidatedoverayearperiod,withresultsfromtwo

Three-daytests(summerandwinter)presentedhere.Table3

sum-marisestheresults.

Itcanbeobservedthatcomparedtogoodtemperature

corre-lations(>90%),thepredictedpositioningofthemachinematched

within60–67%rangewiththemeasuredmovement.Thisis

sus-pectedtobeduetotheaveragedheattransfercoefﬁcientvalues

usedinthis casestudyfortheFEAmodel.Itis anticipatedthat

thepositioningresultscancorrelatebetterwhentheFEAmodel

isappliedwithsurfacespeciﬁcheattransfercoefﬁcientsthatvary

aroundenclosedvoidscreatingairpocketsthatwillvaryin

tem-peratureindependenttothebulkambienttemperature[1].

5. Conclusions

Environmentalthermaltestingisoftenavoidedinindustriesdue

tothecostsandinconvenienceassociatedwithmachinedowntime.

Thispaperpresentedanovelofﬂineenvironmentalthermalerror

modellingmethodbasedonFEAthatsuccessfullydealswiththe

machine downtimeissueusinga two-stagesimulation method,

shorton-linetesting periodand non-disruptiveofﬂine

tempera-turemonitoring.ThesequenceofthemethodistocreateaCAD

modelofthemachine,determinethesettlingtimeofthatmachine

modelandcreateinitialconditionsintheﬁrststagefollowedby

theenvironmentalsimulationinthesecondstage.Thesettlingtime

ensurestheminimumtimeisspentondataacquisition.

Tempera-turesensorscanbeinstalledonthemachineduringanyconvenient

scheduledmachinemaintenanceandthesimulationscanbedone

withinanhourortwo,soitishighlyefﬁcient.Themethodology

wassuccessfullyvalidatedona3axisverticalmillingmachinetool

overayearperiod;samplesofdatafromtwoETVEtestsduring

twoseasons(summerandwinter)arepresentedwherethecritical

natureoftheﬂuctuatingshopﬂoorenvironmentanditseffecton

machinetoolprecisionwerealsohighlighted.Theresultsrevealed

goodcorrelations betweentheexperimentaland FEAsimulated

resultstypicallybetween60%and70%.Themodellingmethodology

hassigniﬁcantlyreducedthemachinedowntimerequiredfora

typ-icalenvironmentaltestingfromafortnighttoonlyhours.Practically

nomachinedowntimeisassociatedwiththeapplicationofthis

modellingmethodologyexceptforshortvalidations(ifrequired).

Additionalusefulinformationcanbeobtainedforpredictingthe

effectsofspeculativeconditions.

Acknowledgements

TheauthorsgratefullyacknowledgetheUK’sEngineeringand

PhysicalSciences ResearchCouncil(EPSRC) fundingof the

Cen-trefor AdvancedMetrology underitsinnovativemanufacturing

programme.

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